Full Controlled Rectifier

Full Controlled Rectifier with R Load

If α= 0° ,The output will be same as a Full Uncontrolled Rectifier that uses DIODE.
Average Load/Output Voltage


{V_0} = \frac{2}{{2\pi }}\int_\alpha ^\pi  {\sqrt 2 V\sin \theta d\theta }

      = \frac{{\sqrt 2 V}}{\pi }\left( {1 + \cos \alpha } \right)
Average Load/Output Current


{I_0} = \frac{{{V_0}}}{R}
 

Full Controlled Rectifier with R Load
Full Controlled Rectifier with DC Motor Load
For 90° < α < 180°

Full Controlled Rectifier with DC Motor LoadAverage Load/Output Voltage
{V_0} = \frac{2}{{2\pi }}\int_\alpha ^{\pi  + \alpha } {{V_m}\sin \theta d\theta }
          = \frac{{2{V_m}}}{\pi }\cos \alpha
Average Load/Output Current
Vo = IoRa + Ea
Ea = armature back emf.
For 90° < α < 180°
Full Controlled Rectifier with DC Motor Load Converter Output Characteristics for continuous load current

Converter Output Characteristics for continuous load current

For fully controlled rectifier, the DC Motor operates in two modes.
1. Rectification [As Motoring]
V0 = positive
Ea = Positive
Io= positive
Power Flow (+ve) from input AC to DC machine
2. Inversion [As Regenerative Braking]
V0 = negative
Ea = negative
Io= positive
Power Flow (-ve) from DC machine to AC supply

The output voltage can be varied from a maximum of 2Vm/π to a minimum of zero as the firing angle a varies from zero to π. The rms output voltage is given by
{V_{rms}} = {\left[ {\frac{2}{{2\pi }}\int\limits_\alpha ^\pi  {V_m^2{{\sin }^2}\omega td\left( {\omega t} \right)} } \right]^{\frac{1}{2}}}
{V_{rms}} = \frac{{{V_m}}}{{\sqrt 2 }}{\left[ {\frac{1}{\pi }\left( {\pi  - \alpha  + \frac{{\sin 2\alpha }}{2}} \right)} \right]^{\frac{1}{2}}}
previous Performance of Single-phase, half-wave controlled rectifiers
next Single-Phase Full Converter with RL load

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